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Chapter 3 Digital Logic Structures

Chapter 3 Digital Logic Structures. Transistor: Building Block of Computers. Microprocessors contain millions of transistors Intel Pentium II: 7 million Compaq Alpha 21264: 15 million Intel Pentium III: 28 million Intel Pentium4: 55 Million Intel Core 2 Duo: 291 Million

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Chapter 3 Digital Logic Structures

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  1. Chapter 3Digital LogicStructures

  2. Transistor: Building Block of Computers • Microprocessors contain millions of transistors • Intel Pentium II: 7 million • Compaq Alpha 21264: 15 million • Intel Pentium III: 28 million • Intel Pentium4: 55 Million • Intel Core 2 Duo: 291 Million • Logically, each transistor acts as a switch • Combined to implement logic functions • AND, OR, NOT • Combined to build higher-level structures • Adder, multiplexor, decoder, register, … • Combined to build processor • LC-3

  3. Transistors http://www.brew-wood.co.uk/computers/transistor.htm A 2011 processor with 1.17 billion transistors positioned in 240 sq. millimeters First transistor: Bell Labs in 1947; developed by J. Bardeen, W. Shockley & W. Brattain

  4. Simple Switch Circuit • Switch open: • No current through circuit • Light is off • Vout is +2.9V • Switch closed: • Short circuit across switch • Current flows • Light is on • Vout is 0V Switch-based circuitscan easily represent two states: on/off, open/closed, voltage/no voltage.

  5. N-type MOS Transistor • MOS = Metal Oxide Semiconductor • two types: N-type and P-type • N-type • when Gate has positive voltage,short circuit between #1 and #2(switch closed) • when Gate has zero voltage,open circuit between #1 and #2(switch open) Gate = 1 Drain Animation Gate = 0 Source GND Terminal #2 must be connected to GND (0V). GND

  6. P-type MOS Transistor • P-type is complementary to N-type • when Gate has positive voltage,open circuit between #1 and #2(switch open) • when Gate has zero voltage,short circuit between #1 and #2(switch closed) Gate = 1 +2.9V GND Source Gate = 0 Drain Terminal #1 must be connected to +2.9V.

  7. CMOS Circuit • Complementary MOS • Uses both N-type and P-type MOS transistors • P-type • Attached to + voltage • Pulls output voltage UP when input is zero • N-type • Attached to GND • Pulls output voltage DOWN when input is one • For all inputs, make sure that output is either connected to GND or to +,but not both!

  8. Inverter (NOT Gate) High Voltage Truth table Ground

  9. Logical Operations • In 1850, George Boole developed Boolean Algebra showing that all logical functions can be performed with just 3 operations (AND, OR & NOT). In 1937, Claude Shannon showed that Boolean Algebra could be applied to circuit design. http://www.computerhistory.org/revolution/digital-logic/12/269

  10. NOR Gate (NOT OR) High Voltage Ground Note: Serial structure on top, parallel on bottom.

  11. OR Gate Add inverter to NOR.

  12. NAND Gate (NOT-AND) Note: Parallel structure on top, serial on bottom.

  13. AND Gate Add inverter to NAND.

  14. Basic Logic Gates

  15. More than 2 Inputs? • AND/OR can take any number of inputs. • AND = 1 if all inputs are 1. • OR = 1 if any input is 1. • Similar for NAND/NOR. • An AND gate with k inputs is called and ANDk gate (e.g., an AND2, AND3, etc). • Can implement AND3 with multiple AND2 gates,or with single transistor circuit. • AND/OR are associative and commutative -- combine in any order.

  16. Logical Completeness • Can implement ANY truth table with AND, OR, NOT. • AND combinations that yield a "1" in the truth table. • Put a “bubble” (inverter) for every 0, a straight-in for every 1 in a row 2. OR the resultsof the AND gates. If there are N 1’s, there will be N and gates; the or gate will have N inputs

  17. DeMorgan's Law • Converting AND to OR (with some help from NOT) • Consider the following gate: To convert AND to OR (or vice versa), invert inputs and output. Same as A OR B!

  18. Summary • MOS transistors are used as switches to implementlogic functions. • N-type: connect to GND, turn on (with 1) to pull down to 0 • P-type: connect to +2.9V, turn on (with 0) to pull up to 1 • Basic gates: NOT, NOR, NAND • Logic functions are usually expressed with AND, OR, and NOT • Properties of logic gates • Completeness • can implement any truth table with AND, OR, NOT • DeMorgan's Law • convert AND to OR by inverting inputs and output

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